Items will only be bought if there is enough coin available to fill the entire order. If you try to buy high-end items that cost a lot in bulk you may come up short, even if you have 2 mil.
As for selling items. You have to set the item that should be sold by clicking on the attachment near the front of the building and selecting the item. You can't just place any item in the storage, you have to select which item is sold.
The conditions for buying and selling each day are checked twice every game day, if during the check conditions are not met there will be no buying or selling until the next check. This also means that if the service is not working (because of no energy or no private citizens available) it will not work.